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Concept module

Pressure and Hydrostatic Pressure

Use one piston-and-tank bench to connect force per area, pressure acting in all directions, and the way density, gravity, and depth build hydrostatic pressure.

Interactive lab

Keep the stage, graph, and immediate control feedback in one working view.

Use the piston load to set a surface pressure, then change depth, density, or gravity. The probe readout, equal-direction arrows, and response graphs stay tied to one static tank.

Graphs

Switch graph views without breaking the live stage and time link.

Pressure vs depth

Hold force, area, density, and gravity fixed while moving only the probe depth. The hydrostatic and total curves rise linearly, while the surface-pressure line stays flat.

depth (m): 0.2 to 4pressure (kPa): 0 to 64

Surface pressureHydrostatic gainProbe pressure

Hover or scrub to link the graph back to the stage.depth (m) / pressure (kPa)

Controls

Adjust the physical parameters and watch the motion respond.

Surface force

F

720 N

Changes the piston load at the fluid surface.

Piston area

A

0.15 m^2

Spreads the same force across a wider or narrower surface.

Fluid density

ρ

1e3 kg/m^3

Sets how much pressure each meter of depth adds.

Gravity

g

9.8 m/s²

Changes the hydrostatic pressure gradient without changing $F/A$.

More tools

Secondary controls, alternate presets, and less-used toggles stay nearby without crowding the main bench.

Hide

Probe depth

h

1 m

Moves the probe deeper or shallower in the same fluid.

More presets

Presets

Predict -> manipulate -> observe

Keep the active prompt next to the controls so each change has an immediate visible consequence.

ObservationPrompt 1 of 5

Drag the probe deeper. The surface pressure from

F / A

does not change, but the total probe pressure grows because the hydrostatic piece

ρ g h

is larger.

Equation map

See each variable before you move it.

Select a symbol to highlight the matching control and the graph or overlay it most directly changes.

F

Surface force

720 N

Changes the total push on the piston. At fixed area it changes only the surface-pressure part of the probe reading.

Graph: Pressure vs forceOverlay: Surface load

Equations in play

Choose an equation to sync the active symbol, control highlight, and related graph mapping.

More tools

Detailed noticing prompts, guided overlays, and challenge tasks stay available without taking over the main bench.

Hide

What to notice

Use one concrete pressure question at a time so the piston load, fluid depth, and graphs stay tied together.

ObservationPrompt 1 of 5

Graph: Pressure vs depth

Drag the probe deeper. The surface pressure from

F / A

does not change, but the total probe pressure grows because the hydrostatic piece

ρ g h

is larger.

Control: Probe depthGraph: Pressure vs depthOverlay: Depth guideOverlay: Pressure arrowsEquation

h

Guided overlays

Focus one overlay at a time to see what it represents and what to notice in the live motion.

4 visible

Overlay focus

Surface load

Shows the piston area and the downward surface force that creates $F/A$.

What to notice

Changing area changes the piston width, so the same force can produce a smaller pressure when it is spread out.

Why it matters

It keeps pressure tied to force per area instead of treating pressure as a mysterious extra quantity.

Control: Surface forceControl: Piston areaGraph: Pressure vs forceGraph: Pressure vs areaEquation

F

Equation

A

Challenge mode

Use the same static tank for direct pressure targets and compare matches. The checks read the live pressure components instead of switching to a separate challenge model.

0/2 solved

MatchCore

6 of 8 checks

Hit 24 kPa by depth alone

Start from Water baseline and adjust only the probe depth until the total pressure is about 24 kPa while the piston load, area, density, and gravity stay near baseline.

Graph-linkedGuided start2 hints

Suggested start

Keep the surface-loading controls and fluid properties near the baseline while you move only the probe.

Matched

Open the pressure-depth graph.

Pressure vs depth

Matched

Keep the depth guide visible.

Matched

Keep the force near the baseline.

720 N

Matched

Keep the area near the baseline.

0.15 m^2

Matched

Keep the fluid near water density.

1e3 kg/m^3

Matched

Keep gravity near Earth gravity.

9.8 m/s²

Pending

Move the probe to about 1.96 m depth.

1 m

Pending

Reach about 24 kPa total pressure.

14.6 kPa

The checklist updates from the live simulation state, active graph, overlays, inspect time, and compare setup.

A surface force of 720 N spread over 0.15 m^2 creates 4.8 kPa of surface pressure. In a water-like fluid at 9.8 m/s², moving to depth 1 m adds 9.8 kPa, so the probe reads 14.6 kPa. The pressure gradient is 9.8 kPa/m. Most of the probe reading comes from the weight of the fluid above the probe, not from the surface load alone. The probe is still near the surface, so the hydrostatic gain is present but not yet dominant.

Equation detailsDeeper interpretation, notes, and worked variable context.

Pressure from a surface load

The same force gives less pressure when it is spread over a larger area.

P_{s} = \frac{F}{A}

F

Surface force 720 N

A

Piston area 0.15 m^2

Hydrostatic pressure

Depth adds pressure because deeper points support more fluid above them.

P_{h} = ρ g h

ρ

Fluid density 1e3 kg/m^3

g

Gravity 9.8 m/s²

h

Probe depth 1 m

Total probe pressure

The probe reads the transmitted surface pressure plus the depth-dependent hydrostatic contribution.

P_{probe} = P_{s} + P_{h}

F

Surface force 720 N

A

Piston area 0.15 m^2

ρ

Fluid density 1e3 kg/m^3

g

Gravity 9.8 m/s²

h

Probe depth 1 m

Pressure change with depth

Each extra depth step adds the same pressure increment when density and gravity stay fixed.

Δ P = ρ g Δ h

This is the linear hydrostatic pressure gradient for the bounded static-fluid model on this page.

ρ

Fluid density 1e3 kg/m^3

g

Gravity 9.8 m/s²

h

Probe depth 1 m

Progress

Not startedMastery: NewLocal-first

Start exploring and Open Model Lab will keep this concept's progress on this browser first. Challenge mode has 2 compact tasks ready. No finished quick test, solved challenge, or completion mark is saved yet.

Let the live model runChange one real controlOpen What to notice

Try this setup

Copy the live bench state and reopen this concept with the same controls, graph, overlays, and compare context.

Stable links

Starter track

Step 1 of 50 / 5 complete

Fluid and Pressure

Next after this: Continuity Equation.

1. Pressure and Hydrostatic Pressure2. Continuity Equation3. Bernoulli's Principle4. Buoyancy and Archimedes' Principle+1 more steps

This concept is the track start.

See next concept

Short explanation

What the system is doing

Pressure starts as force per unit area. If the same push is spread over a larger area, each square meter gets a smaller share of that push. On this bench, the piston at the fluid surface makes that idea visible before depth is added.

A fluid at rest transmits pressure throughout the connected fluid, and at one point that pressure acts equally in all directions. The probe arrows do not point only downward because hydrostatic pressure is not a downward force rule. It is a scalar pressure field that can later create net forces only when pressure differs from one place to another.

Hydrostatic pressure grows with depth because deeper points support more fluid above them. In this bounded model, the probe reading is the surface pressure from $F / A$ plus the depth-dependent gain $ρ g h$ . That keeps force, area, density, gravity, depth, graphs, compare mode, prediction prompts, worked examples, and challenge checks attached to one honest static-fluid story without expanding into a full fluid-mechanics platform.

Key ideas

01Pressure from a surface load is force divided by area, so the same force gives a smaller pressure when it is spread across a wider piston.

02In a resting connected fluid, pressure at one point acts equally in all directions and points at the same depth share the same hydrostatic contribution.

03Hydrostatic pressure increases linearly with depth because each extra meter adds another $\rho g$ of pressure.

04Density and gravity set the slope of the pressure-depth graph, which is why denser fluids or stronger gravity produce larger pressure differences over the same height.

Live pressure checks

Solve the exact state on screen.

Use the current tank directly. The same piston load, fluid properties, and probe depth now on screen drive both worked examples, so the algebra stays tied to the live visualization.

Live valuesFollowing current parameters

For the current tank with $F = 720$ , $A = 0.15$ , $ρ = 1 e 3$ , $g = 9.8$ , and $h = 1$ , what pressure should the probe read?

F

Surface force

720 N

A

Piston area

0.15 m^2

ρ

Fluid density

1e3 kg/m^3

g

Gravity

9.8 m/s²

h

Probe depth

1 m

1. Turn the piston load into surface pressure

The piston sets

P_{s} = F / A = 4.8 kPa

, so the same force is currently being spread across a moderate piston area.

2. Add the hydrostatic contribution from depth

The fluid column contributes

P_{h} = ρ g h = 9.8 kPa

at depth

1 m

3. Combine the two contributions

So the probe reads

P_{probe} = P_{s} + P_{h} = 14.6 kPa

, with the hydrostatic contribution currently larger.

Current probe pressure

P_{s} = 4.8 kPa, P_{h} = 9.8 kPa, P_{probe} = 14.6 kPa

The fluid column is doing most of the work here, so moving deeper or changing density would matter more than changing the same already-moderate surface load.

Fluid statics checkpoint

Two pressure probes are held at the same depth in the same resting fluid, but one is near the wall and the other is near the center. Which reads higher?

Prediction prompt

Decide whether sideways position matters once fluid, depth, gravity, and surface loading are all the same.

Check your reasoning

They read the same pressure.

In one connected resting fluid, the hydrostatic part depends on depth, density, and gravity. Sideways position does not create a second pressure law. Later buoyancy comes from different depths on the same object, not from a special sideways pressure rule.

Common misconception

Fluid pressure only pushes downward because the fluid is above the point you are looking at.

The fluid weight above a point explains why pressure grows with depth, but the pressure at that point acts equally in all directions.

That is why the same-depth line matters, and why later buoyancy comes from pressure being larger on deeper parts of an object than on shallower parts.

Quick test

Variable effect

Question 1 of 5

Answer from the tank, not from a slogan. The goal is to keep pressure causal and visual.

At the same force, what happens if the piston area is increased?

Choose one answer to reveal feedback, then test the idea in the live system if a guided example is available.

Accessible description

The simulation shows one piston pressing on a fluid tank and one probe at an adjustable depth. The piston width represents area, the downward arrow represents surface force, the probe depth marker shows how far below the surface the point is, and equal-length arrows around the probe show pressure acting equally in all directions at that point.

The readout card reports force, area, surface pressure, density, gravity, depth, hydrostatic pressure, and total probe pressure. Compare mode ghosts one second setup so the same tank can show two different ways to reach similar pressures.

All graphs on this page are response graphs for a static fluid. One graph varies depth, one varies density, one varies force, and one varies piston area while the other variables stay fixed.

Graph summary

The pressure-depth graph is the main hydrostatic graph. The surface-pressure line stays flat while the hydrostatic and total curves rise linearly with depth.

The density, force, and area graphs isolate the other levers. Density changes only the hydrostatic part, force changes only the surface-pressure part, and area changes the same surface load by spreading it out more or less.

Carry this into buoyancy and fluids

Keep moving through the concept map.

These suggestions come from the concept registry, so the reason label reflects either curated guidance or the fallback progression logic.

Move from static pressure to steady flowFluids

Pressure and Hydrostatic Pressure

See each variable before you move it.

Surface load

Hit 24 kPa by depth alone

Fluid and Pressure

What the system is doing

Solve the exact state on screen.

For the current tank with F=720, A=0.15, ρ=1e3, g=9.8, and h=1, what pressure should the probe read?

At the same force, what happens if the piston area is increased?

Keep moving through the concept map.

Continuity Equation

Bernoulli's Principle

Buoyancy and Archimedes' Principle

For the current tank with $F = 720$ , $A = 0.15$ , $ρ = 1 e 3$ , $g = 9.8$ , and $h = 1$ , what pressure should the probe read?